The language of higher dimensional categories (LHDC)
- Kód projektu
- Období řešení
- 7/2021 - 6/2024
- Investor / Programový rámec / typ projektu
- Masarykova univerzita
- Fakulta / Pracoviště MU
- Přírodovědecká fakulta
Category theory is the language that expresses the common features of, and relationships between, different areas of mathematics. It is fundamental in modern algebra and topology, where it governs key notions such as homotopy and homology. Beyond pure mathematics, it is used in diverse areas such as the design of functional programming languages,
computational linguistics and theoretical physics via topological quantum field theories.
Recently there have been rapid developments in the young field of higher
dimensional category theory, which concerns the study of relationships between relationships and so on ad infinitum. Due to the complexity of these infinite dimensional structures, the technical details are demanding, and the main
texts span thousands of pages. The goal of this project is to develop new
low dimensional approaches to higher dimensional category theory, which will
make it more accessible to researchers from diverse fields, and lead to new
applications in pure mathematics and beyond.